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If S is an infinite set, then the collection F_S={A subset= S:S-A is finite} is a filter called the cofinite (or Fréchet) filter on S.

Given a set S of points in the plane, an enclosing circle is a circle for which all points S lie in its interior.

A group G is said to be finitely generated if there exists a finite set of group generators for G.

The homeomorphism group of a topological space X is the set of all homeomorphisms f:X->X, which forms a group by composition.

The map which assigns every member of a set A to the same element id_A. It is identical to the identity function.

A set of graph vertices A of a graph with graph edges V is independent if it contains no graph edges.

"The integers" is a common way of referring to the set of integers, commonly denoted Z.

Given a positive integer n, a labeled n-digraph is a digraph whose vertex set is {1,...,n}.

A number theoretic function is a function whose domain is the set of positive integers.

"The reals" is a common way of referring to the set of real numbers and is commonly denoted R.